Space of modular forms of level 2550, weight 2, and trivial character

• Label: 2550.2.a
• Level: $2550$
• Weight: $2$
• Character orbit: 2550.a
• Rep. character: $\chi_{2550}(1,\cdot)$
• Character field: $\Q$
• Dimension: $52$
• Newform subspaces: $41$
• Sturm bound: $1080$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 41 \)
Sturm bound:			\(1080\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2550))\).

	Total	New	Old
Modular forms	564	52	512
Cusp forms	517	52	465
Eisenstein series	47	0	47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(5\)	\(17\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(30\)	\(3\)	\(27\)		\(28\)	\(3\)	\(25\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(39\)	\(3\)	\(36\)		\(36\)	\(3\)	\(33\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(39\)	\(2\)	\(37\)		\(36\)	\(2\)	\(34\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(33\)	\(4\)	\(29\)		\(30\)	\(4\)	\(26\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(36\)	\(4\)	\(32\)		\(33\)	\(4\)	\(29\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(33\)	\(2\)	\(31\)		\(30\)	\(2\)	\(28\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(36\)	\(3\)	\(33\)		\(33\)	\(3\)	\(30\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(36\)	\(5\)	\(31\)		\(33\)	\(5\)	\(28\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(33\)	\(3\)	\(30\)		\(30\)	\(3\)	\(27\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(39\)	\(2\)	\(37\)		\(36\)	\(2\)	\(34\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(36\)	\(4\)	\(32\)		\(33\)	\(4\)	\(29\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(33\)	\(4\)	\(29\)		\(30\)	\(4\)	\(26\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(36\)	\(2\)	\(34\)		\(33\)	\(2\)	\(31\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(36\)	\(5\)	\(31\)		\(33\)	\(5\)	\(28\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(36\)	\(5\)	\(31\)		\(33\)	\(5\)	\(28\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(33\)	\(1\)	\(32\)		\(30\)	\(1\)	\(29\)		\(3\)	\(0\)	\(3\)
Plus space				\(+\)		\(276\)	\(21\)	\(255\)		\(253\)	\(21\)	\(232\)		\(23\)	\(0\)	\(23\)
Minus space				\(-\)		\(288\)	\(31\)	\(257\)		\(264\)	\(31\)	\(233\)		\(24\)	\(0\)	\(24\)

Trace form

52 * q + 2 * q^3 + 52 * q^4 - 2 * q^6 + 52 * q^9 - 8 * q^11 + 2 * q^12 - 8 * q^14 + 52 * q^16 + 8 * q^19 + 20 * q^21 - 8 * q^23 - 2 * q^24 + 2 * q^27 - 16 * q^29 + 24 * q^31 - 8 * q^33 - 4 * q^34 + 52 * q^36 - 8 * q^37 + 8 * q^38 + 28 * q^39 - 16 * q^41 - 4 * q^42 - 8 * q^43 - 8 * q^44 - 8 * q^46 - 16 * q^47 + 2 * q^48 + 76 * q^49 - 2 * q^51 - 16 * q^53 - 2 * q^54 - 8 * q^56 + 16 * q^57 + 16 * q^58 - 40 * q^59 + 8 * q^61 - 24 * q^62 + 52 * q^64 + 8 * q^66 + 32 * q^67 + 4 * q^69 + 8 * q^71 + 32 * q^73 + 16 * q^74 + 8 * q^76 + 4 * q^78 + 8 * q^79 + 52 * q^81 + 24 * q^82 + 24 * q^83 + 20 * q^84 + 8 * q^87 + 48 * q^91 - 8 * q^92 + 36 * q^93 - 2 * q^96 + 40 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2550))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	5	17
2550.2.a.a	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(-3\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
2550.2.a.b	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				510.2.a.g	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
2550.2.a.c	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				102.2.a.c	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2550.2.a.d	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				510.2.a.f	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2550.2.a.e	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.e	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2550.2.a.f	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.f	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots\)
2550.2.a.g	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.g	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(5\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots\)
2550.2.a.h	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.h	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
2550.2.a.i	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				510.2.a.d	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
2550.2.a.j	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.j	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
2550.2.a.k	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.k	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
2550.2.a.l	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				510.2.a.e	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
2550.2.a.m	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.m	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
2550.2.a.n	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				510.2.a.c	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
2550.2.a.o	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				510.2.d.a	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
2550.2.a.p	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.p	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
2550.2.a.q	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.q	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
2550.2.a.r	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.p	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
2550.2.a.s	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				510.2.d.a	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
2550.2.a.t	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.q	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
2550.2.a.u	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				102.2.a.b	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
2550.2.a.v	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.m	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
2550.2.a.w	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.j	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
2550.2.a.x	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.k	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
2550.2.a.y	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				510.2.a.b	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
2550.2.a.z	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.h	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
2550.2.a.ba	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.g	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-5\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-5q^{7}+q^{8}+\cdots\)
2550.2.a.bb	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓	✓	✓	2550.2.a.f	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
2550.2.a.bc	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				510.2.a.a	$1$	$1$	\(1\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
2550.2.a.bd	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.e	$1$	$0$	\(1\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
2550.2.a.be	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓				102.2.a.a	$1$	$0$	\(1\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
2550.2.a.bf	$2550$	$2$	2550.a	1.a	$1$	$1$	$1$	$20.362$	\(\Q\)	None	✓	✓			2550.2.a.a	$1$	$0$	\(1\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
2550.2.a.bg	$2550$	$2$	2550.a	1.a	$1$	$2$	$2$	$20.362$	\(\Q(\sqrt{33}) \)	None	✓	✓	✓		2550.2.a.bg	$1$	$0$	\(-2\)	\(-2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-\beta q^{7}-q^{8}+\cdots\)
2550.2.a.bh	$2550$	$2$	2550.a	1.a	$1$	$2$	$2$	$20.362$	\(\Q(\sqrt{5}) \)	None	✓		✓		510.2.d.b	$1$	$1$	\(-2\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta )q^{7}+\cdots\)
2550.2.a.bi	$2550$	$2$	2550.a	1.a	$1$	$2$	$2$	$20.362$	\(\Q(\sqrt{6}) \)	None	✓		✓		510.2.d.c	$1$	$0$	\(-2\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{6}+\beta q^{7}-q^{8}+\cdots\)
2550.2.a.bj	$2550$	$2$	2550.a	1.a	$1$	$2$	$2$	$20.362$	\(\Q(\sqrt{6}) \)	None	✓		✓		510.2.d.c	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+\beta q^{7}+q^{8}+\cdots\)
2550.2.a.bk	$2550$	$2$	2550.a	1.a	$1$	$2$	$2$	$20.362$	\(\Q(\sqrt{5}) \)	None	✓		✓		510.2.d.b	$1$	$0$	\(2\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta )q^{7}+\cdots\)
2550.2.a.bl	$2550$	$2$	2550.a	1.a	$1$	$2$	$2$	$20.362$	\(\Q(\sqrt{6}) \)	None	✓		✓		510.2.a.h	$1$	$0$	\(2\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta q^{7}+q^{8}+\cdots\)
2550.2.a.bm	$2550$	$2$	2550.a	1.a	$1$	$2$	$2$	$20.362$	\(\Q(\sqrt{33}) \)	None	✓	✓			2550.2.a.bg	$1$	$0$	\(2\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta q^{7}+q^{8}+\cdots\)
2550.2.a.bn	$2550$	$2$	2550.a	1.a	$1$	$3$	$3$	$20.362$	3.3.568.1	None	✓		✓		510.2.d.d	$1$	$1$	\(-3\)	\(-3\)	\(0\)	\(-6\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
2550.2.a.bo	$2550$	$2$	2550.a	1.a	$1$	$3$	$3$	$20.362$	3.3.568.1	None	✓		✓		510.2.d.d	$1$	$0$	\(3\)	\(3\)	\(0\)	\(6\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{6}+(2+\beta _{1})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2550))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2550)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1275))\)\(^{\oplus 2}\)